Quadratic Transformations

Front

What is a quadratic transformation?

Back

A quadratic transformation refers to the changes made to the graph of a quadratic function, such as stretching, compressing, or shifting it in the coordinate plane.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How does a vertical stretch affect the graph of a quadratic function?

Back

A vertical stretch occurs when the coefficient 'a' in the vertex form is greater than 1, making the graph narrower.

Front

How does a vertical compression affect the graph of a quadratic function?

Back

A vertical compression occurs when the coefficient 'a' in the vertex form is between 0 and 1, making the graph wider.

Front

What does shifting a graph up mean?

Back

Shifting a graph up means adding a positive value to the function, which moves the entire graph upwards on the y-axis.

Front

What does shifting a graph down mean?

Back

Shifting a graph down means subtracting a positive value from the function, which moves the entire graph downwards on the y-axis.

Front

What does shifting a graph left mean?

Back

Shifting a graph left means subtracting a value from 'x' in the function, which moves the entire graph to the left on the x-axis.

Front

What does shifting a graph right mean?

Back

Shifting a graph right means adding a value to 'x' in the function, which moves the entire graph to the right on the x-axis.

Front

If the equation is y = 2(x+2)² - 5, what transformations are applied?

Back

The graph is stretched vertically by a factor of 2, shifted 2 units left, and 5 units down.

Front

What is the effect of a negative 'a' value in a quadratic function?

Back

A negative 'a' value reflects the graph across the x-axis, making it open downwards.